Why does coil feel warm?

Back in the day the dist could end up with the points open or closed when the engine is shut off. If they happen to be closed, and you turn the key to run, the coil (as others have said) will be in a charge condition, consuming energy and turning it to heat.

One function of the ballast resister is to limit the current going to the coil to help keep it from overheating.(at least that's how I understand it)